The American parents accused of fleeing to Cuba with their kidnapped sons are being isolated at a Florida jail for their safety as they await their first court date, a jail official told ABCNews.com.

Although Joshua Hakken, 35, and Sharyn Hakken, 34, are being held in their own cells at the Hillsborough County Jail, they are receiving no special treatment, Corporal Howard Lindsey said.

"In any case that is high profile, when they first arrive here we try to segregate them from the general population until the hype calms down," Lindsey said.

The Hakkens were returned to the United States early this morning in the custody of FBI agents before they were booked into the Hillsborough County Jail.

Their sons, Cole 4, and Chase, 2, who were also on board the flight from Cuba, were returned to the custody of their maternal grandparents.

A few hours before the plane landed, authorities held a news conference and said both parents are facing kidnapping, child interference with child custody and neglect charges. Joshua Hakken is facing grand theft auto, false imprisonment, battery and burglary. Hakken is also facing a federal charge for unlawful flight to avoid prosecution. The couple is scheduled to make their first court appearance on Thursday.

The children had been living with their maternal grandparents in Tampa, Fla., until last Wednesday, when authorities allege that Joshua Hakken barged into the home, tied up his mother-in-law, and fled with his sons in her car.

The children's grandparents, Bob and Patricia Hauser, were also at the news conference, and said they had a phone conversation with their grandsons shortly before they departed for the United States.

"Please continue to respect our privacy as we reunite with our precious grandchildren," Bob Hauser said. "Right now we're just looking forward to sitting and getting them in our arms and hugging them and being with them getting them home where they will be safe again."

Hillsborough County Sheriff David Gee said the kids appear fine.

"Our understanding is that they're doing well and we're looking at them from a medical standpoint and all that will be checked out," Gee said.

A team of FBI agents departed the Tampa area at 10 p.m. Tuesday and met with authorities in Cuba.

FBI special agent David Couvertier said the U.S. State Department received information the family was in Cuba.

Couvertier said they treated the alleged kidnapping as a "hostage situation" and did not consider it "typical."

The Hakkens arrived in the Hemingway Marina in Havana April 7 aboard their sailboat, Salty Paw, under unfavorable sailing conditions, according to a statement from the Cuban Foreign Ministry.

The next day, Cuban officials said they became aware the Hakkens were wanted in an abduction case and contacted U.S. officials in Havana.

Cuba does not have an extradition treaty with the United States, but the Cuban Foreign Ministry said it remained in frequent diplomatic communication with the U.S. Interests Section in Havana regarding the situation.

The Hakken family was spotted by ABC News Tuesday getting off the boat in Havana and being escorted by government officials. Joshua Hakken and his sons were accompanied to a restaurant on the marina by dozens of Cuban government officials, while Sharyn Hakken was seen being driven away in a government vehicle, according to an ABC News producer in Havana.

The Hakkens lost custody of their sons last year after Slidell, La., police found them in a hotel room with their boys surrounded by weapons, drugs and "acting in a bizarre manner."

After Joshua Hakken's boys were placed into protective custody last year, authorities said he showed up at their foster home banging on the door with a gun, demanding his two sons. Authorities said he fled the scene when the foster parents called 911.

The family dog, a terrier, was also found with the Hakkens in Cuba. Authorities say they have custody of the dog and it will be given to the boys once they land.